Flourishing fountains fanfare out of a still pond

    
Quantum Mechanics is the science that studies the sub-atomic particles and deals with the behavior of objects within their Compton wavelengths.

While studying quantum mechanics, there are five points to keep mind.

First, more than eighty years of lab experiments proved that the principles of quantum mechanics are real and valid. Mathematics of quantum theory precisely predicts and reproduces the results of physical experiments. We are applying these principles in making delicate instruments and building precise computers. Therefore, Quantum Mechanics is an actual science.

Second, Quantum mechanics is weird. In this arena, certainty of classic physics is replaced by the uncertainty and definite state observed in macro-world turns to chaotic world of super-position of states. Casualty (cause and effect) may reverse so that cause appears before effect (second Feynman diagram). Direction of time can reverse also and future arrives before the past. Entanglement between distant particles exists without apparent link. The law of conservation of energy gets pale in many instances. And so forth and so on.

Third, apparently we cannot utilize the logic of classical physics to interpret the weirdness of quantum mechanical phenomena. We have to develop a new logic to accommodate a reality that is beyond our today's consensus reality.

Fourth, quantum physics is not an abstract science that belongs to laboratories and scientists, it is the basic building blocks of our body and our macro-world and the infra-structure of laws of classical physics.

And fifth, Quantum mechanics laws are applied equally to micro and macro-world.

Hypothesis

Quantum arena is the twilight zone between space-time
and
the proposed non-local energy-information mind-like singularity.

One of the main tasks of this model is to propose explanations for unexplained findings in quantum theory. We cannot explain the Schrodinger's cat(explained in coming pages) being alive and dead at the same time, with our conventional logic. Surprisingly though, we can imagine such a superposition in our mind. Not only our imagination can accommodate such a dual and antagonistic state but our mind activity is frequently utilizes superposition in its different functions.

Niels Bohr is the founder of quantum mechanics. His approach to the strange quantum realm was just to observe the experiments results and not trying to find causality for their presence or explain the reality and history behind them. Albert Einstein on the other hand believed that universe is made of real objects with real and definite properties. He believed that Quantum Mechanic theory is deficient and cannot reveal the hidden variables that create strange findings in sub-atomic arena. He further believed that these variables do exist. Einstein believed a deeper theory would find these variables, which are hidden in our experiments. Most physicists have not favored hidden variable theories. Experiments and calculation results contradict these theories. Although Bohemian mechanics (refer to David Bohem) tries to offer an explanation for it.³⁵

Here I am introducing a non-local media, which is connecting different points of space together. Let's see if this model can offer reasonable explanations for different quantum mechanical paradoxes. I hope this model prove to be the Einstein's deeper theory, which explains the quantum mechanical experiments and offers a comprehensible reality. Furthermore, because this model has a mind component, it contains some of the interpretations and views of Neils Bohr as well.

Quantum Mechanic Domain

A particle generally behaves quantum mechanically when observed at distances shorter than its Compton wavelength. Therefore, we can conclude that there is a cut off between classical physics arena and quantum mechanics domain. Please note that we are not choosing below certain distance as a cutoff for quantum mechanical arena. The cut off line is at the edge of the Compton wavelength of any particle. Moreover, wavelengths of different particles are poles apart.

The Compton wavelength (λ) of a particle is given by;

λ = h / m c, where h is the Planck Constant, m is the mass of particle and c is the speed of light.

What is the mystery within the Compton wavelength? It seems something unfamiliar to classic physics is happening inside the wavelength of any particle. This is responsible for weird phenomena that we are observing in quantum mechanics. I have explained my conjectures in the wave-particle function and other previous chapters.

Momentum

In classical physics, momentum is defined as the product of mass (m) and velocity (v) of an object.

P = mv

Simply speaking, momentum is the impact felt by a boxer receiving the opponent’s tossed feast.

The relation between the momentums of an object in regards to its spatial position (x) are obtained by:

P_a = α / αx^a

Where α is a constant. If our object is a subatomic particle then we need to add imaginary number (i) and Dirac constant (ħ) to the equation,

P_a = iħ α / αx^a

The Dirac constant is a reduced Planck Constant (h/2π).

The presence of i indicates that the momentum of a subatomic particle is governed by a complex function. Therefore, the momentum of subatomic particles is periodic (see the complex number chapter). Therefore, the Assertion C2 specifies that the value of the momentum has to hit zero at each period.

The presence of ħ also points out that momentum is directly related to Planck constant. In wave-function chapter, we have assumed that the particle itself disappears and reappears in space-time in each Compton wavelength. We can relate the intermittent blinking of momentum to the intermittent emerging of the particle into the space-time.

Moreover, in the Mass & Gravity chapter we have assumed that the Planck Constant is the amount of kinetic energy carried by the particle upon its arrival into the space-time.

In following paragraphs, we will review the quantum mechanical phenomena while keeping the above conjectures in mind.

Heisenberg Uncertainty Principle

According to Werner K. Heisenberg, the famous German physicist, we cannot simultaneously determine the position and momentum of a particle at ultra short distances. This kind of correlation between two properties is called a complimentarity relation. The equation is written as,

ΔE Δt ≥ h / 2π

In Heisenberg’s famous uncertainty relation for position and momentum, when the position uncertainty changes in position (Δx) is less than the Compton wavelength, the momentum uncertainty changes in momentum (Δp) is greater than h/2π. Since momentum carries energy, the uncertainty in energy is greater than, h/2π. This implies that if we pin point a particle’s location, its momentum can vary widely and therefore we can not be certain about its momentum.

To justify the uncertainty principle, error in measurement and lack of appropriate tool are brought up.Neither is very convincing.

Therefore, quantum theory tells us that we cannot track a subatomic particle by any method whatsoever. Can we assume that, we cannot detect particles because they loose their mass and leave the space-time? Maybe we have to change the sentence as "we cannot track a subatomic particle by any method whatsoever in objective world. The problem arises when we are expecting to see the whole picture in just one arena, (the real number arena). As an analogy, please note that we cannot follow and understand a three dimensional motion in it’s entirely in a two dimensional world. Evan Walker says: “… Heisenberg used matrices (whole array of numbers) to represent the positions and motions of an atomic particle.⁸

In his calculation to create the matrix he used the symbol i which stands for square root of –1, the so called, imaginary number. He had to choose a number, which is out of the domain of our real number system. We cannot ignore the quantity i and call it imaginary.We have to accept that it stands for a kind of reality. According to Dr. Walker quantum mathematics drags us to a scope “that is really an infinity of imaginary worlds.”⁸

Therefore, we have to expand the science domain to include worlds other than familiar space-time. If mathematics so precisely is predicting the mystery world of quantum behavior, we have to value its elements. We have to accept that its unexplained or inapplicable measures to our physical world have an actual meaning.

Let us revisit the location /momentum uncertainty. Please note that one of the elements is spatial and the other is energy related. We can interpret the principle as; when locality gets blurred the energy is more defined. This was explained in the Boundaries Chapter. We also can extend the Heisenberg principle to time and energy in a system.

ΔE Δt ≥ h/ 2π

For example a radioactive atomic nucleus decays with time. If the lifetime of such a state is Δt, then the energy of the exited states is uncertain by:

ΔE ≥ ħ/2π Δt

The second diagram of Feynman for Compton Scattering also leads us to above uncertainty. Here again while t is a spatial element, the other element is energy. As time gets hazy energy gets more distinct and vise versa.

Spectral/Spatial Complemetarity

We can also extend the uncertainty principle to information carried in a beam of light after it passes a lens. Depending on the location of a screen behind the lens, we can either have a sharp image of the object in experiment, or we may come up with a fuzzy image or no image at all. On a proper location every portion of image data has a defined spatial location. Whereas in no image locations the information is carried by light rays are at spectral version and they do not exist in spatial location. Interestingly, in spectral form the data are non local. Which means every small portion of space carries all of the information about our object in hand.

Here we have a complimentarity relation between spectral and spatial features. As we come close to focal point we depart from spectral phase and come to locality. With the same token when we leave focal point we enter spectral phase again and the non-locality prevails. Isn't this a good example for understanding the relation between a spatial local world and non-spatial non-local energy-informatics domain? In our model this paradigm is the proposed singularity.

Information/ Interference Compementarity

George Greenstein and Arthur Zajong mention another very interesting complimentarity relation in their book “The Quantum Challenge”. They explained the complimentarity between information and interference pattern in double slit experiment (see the explanation under the same subtitle in this chapter). Referring to moveable slit modification of the experiment, they wrote:

“Wootters and Zorek have returned to Einstein's modification of the classic double-slit interference experiment, and analyzed it from the stand point of partial information…The slits are free to move. After particle has past through, we measure the slit's momentum… if the slits are moving downward, the particle must have past through slit 2…

Wootters and Zorek noted that the above conclusion is not in fact entirely certain. The same motion of the slits would also be observed had the particle passed the wrong slit --if the initial slit momentum had been large and downward…

They evaluated the probability of the initial slit momentum being large enough to yield such an erroneous conclusion, and so obtained an expression of the probability that we had obtained path information. Using the same wave function, they also calculated the resulting pattern of arrival at the final screen. It turned out to be a partially smeared-out interference pattern”¹¹

Reproduced from Ref. #11 page 101

Their experiment showed that if they had certain knowledge about the slit that particle passed through, there where no interference on screen. But as the uncertainty about the slit increased a better interference were developed.

Looking at different complimentary pairs, the elements for each uncertainty relation are different in that, one of them is either spatial or mass type, and the other is either energy type or informational type. The two characteristic that we hypothesized for proposed singularity.  The fuzzy states of fundamental elements in boundaries of space-time were discussed in Boundaries Chapter.

For details check the link: http://www.upscale.utoronto.ca/
GeneralInterest/Harrison/SchrodCat/SchrodCat.html

Objects in classical physics terms are in a well defined state, whereas in quantum mechanics the objects are not in a definite state. For example, in classic physics an object will rotate either clockwise or counterclockwise. It was shown that in microcosm, a particle is spinning simultaneously in both directions. In other words, a particle concurrently exists in any probable state that is possible. Erwin Schrödinger who first explained the super-position of states offered the analogy of a cat being dead and alive at the same time after the probability of being poisoned is famous and is named after him.

In classical physics terms either the poison is released and cat dies or the poison is contained and cat would be alive. But in quantum mechanics arena, the both outcomes exist simultaneously. This is of course before we open the box. As soon as we open the door we just see one outcome (either a dead or a live cat).

The Schrödinger’s cat is simultaneously dead and alive. Such a sentence does not relay any meaningful concept to us. Or does it?

In the observable world a cat is either dead or alive. The series of events lead to just one of the possibilities.

How are we going to explain this quantum mechanical effect.. Multi universe theories claim that there are different universes that accommodate different possible outcomes, of each action. This is hard to accept. There are countless actions in each miniscule of time in the universe and far more possibilities as well. Possibilities are endless. It means we have to have endless numbers of universes and the number is growing every second at a rate that transcends all concepts of infinitudes. It is also grossly against conservation of energy law if we choose to hold it. This concept is not economical either.

On the other hand, Schrodinger's wave equation which represent the super-position of states, also contains the imaginary factor i. Thus quantum state “will always turn out to contain terms that are imaginary…The complex character of the wave function in Schrodinger's wave equation means that what is there in a sense is hidden from us.”⁸ In other words, Somehow in quantum arena we are exposed to out of space-time realm.

Renormalization in Schrödinger’s Equation

The Schrödinger’s probability equation for the position of a particle during its wave function can be written as:

Ψ * Ψ = Probability

If we believe that the particle is somewhere in space but we cannot exactly pin point it, we can normalize the formula and write:

∫ Ψ * Ψ cr = 1

Which means that we have altered the formula in a way that would show the probability of the particle being somewhere in space is %100. We do this because we believe that everything is confined inside the space-time. So, it is natural to assume that the particle is in space somewhere. Therefore, we write a formula to reflect a normal situation by our space-time logic. If we are revisiting the existing concepts then we are allowed to question normalization as well. Normalization is a major parts of quantum mechanical calculations. If we take normalization out of quantum calculations, we tremble the pillars of its existing mathematics.

Questioning the normalization is similar to questioning the attempts to understand the reality on the basis of space-time properties alone. This is a courageous action. But haven't we been very bold so far? As a matter of fact, solving these great mysteries need enormous amount of daring. At the same time revisiting the calculations can confirm or reject the validity of the singularity concept presented above. It seems that if we redefine the particle wave function to include singularity (a mind like informational domain), we will come to a logical explanation for the phenomena that we are facing. I do not see why we shouldn't let our imagination explore that possibility. Aren't we defining the location of each particle with a complex number, which contains imaginary part as inseparable feature?

Decoherence

Decoherence – the blossom of just one state in macrocosm out of infinite quantum superposition states in micro scale.

We see the world in one definite state. A universe in superposition of states would be an in-deterministic and chaotic world that nobody could stand it. Nothing would remain to rely on or build into it. Even we ourselves would be a total mess. As mixed up as the state that our mind normally is. The proponents of the Decoherence Principle explain why we do not observe superposition of state in our everyday experience. Decoherence principle simply points to the fact that each particle normally exist in an environment. This environment is always bombarded with other particles and photons. The interaction of particles with each other takes them out of super position of state and leaves them in a definite state. That is how the world comes out of confusion and we see one definite state around us.This is a world where we can live and be able to rely on.

State reduction at the margin of the wavelength

Perhaps a better explanation can be obtained by paying attention to the fact that quantum behavior is demonstrated inside the wavelength of each object.

The wavelengths of smaller particles are big enough for us to experimentally observe their superposition of states. The bigger objects on the other hand have a very small and almost undistinguishable wavelength. In this view, the superposition of states takes place within the wavelength of bigger objects.

Singularity, Super Position Domain

If we cannot normally observe the superposition, then where is the most probable place to comprehend it? Where can we find such a cat, which is in superposition of life and death? We assumed singularity to contain information of an object but lacking matter itself. In such a domain, information about any possibility can exist simultaneously. In particle-wave model, I assumed the alternative position of objects in singularity and space-time domain. We can leave superposition of states to singularity and the definite state to space-time. This is how we can avoid the super position conflict with the conservation law.

According to the concept presented, the physical world connects and intermingles with singularity in every miniscule of space. In addition, we have assumed quantum arena (the realm within the wavelength) the interface between our physical world and singularity.

Mind a model for superposition of states

Are we accustomed to superposition of states or is it completely strange to us? Surprisingly, superposition can happen in our mind as well. We are very familiar with superposition of states. In different mind activities such as predicting upcoming events, we imagine different states of proceedings in order to compare and evaluate. When we are planning to make a decision, we picture different mode of possibilities. When we make our decision materializes and the outcome will be just one state.

As a matter of fact, the Copenhagen interpretation of quantum mechanics as first introduced by Neils Bohr implies that superposition of states is a mathematical formalism and exists in the mind of observer. Physical world is the reduced state of the superposition that exists in our mind. So we reduce the super position to one possibility and somehow project it into physical world. See how all of these fall together as different pieces of the same puzzle. Please refer to the three circles of reality presented at the Introduction Chapter. 

Singularity as an informational domain can contain a superposition of states just like our consciousness, which can hold such a superposition. When the particle enters the objective space-time, it is reduced to one state and becomes observable.

Defying the Conservation Law

As mentioned before, if we take superposition as actual objective phenomena, it turns out to be against the dearly loved conservation of energy/matter law. Many discussions and arguments are brought forward by trying to expand super position of states to macroscopic world. One of the main arguments is the many worlds of Everett presented at 1957. It essentially says that for any possible state of any quantum system a new universe will start which accommodates that particular state. Although this interpretation is revoltingly against conservation law and grossly non-economical and beyond belief, it has gained popularity.

In the Consistent History approach to quantum mechanics by Griffith, Omness and Gell-mann/Hartle the superposition state of quantum level is considered a coarse grained state while a projector reduces and refines it to just one state and project it to macroscopic level. According to them this is why we do not observe superposition in macro world. In 1995 Fay Dawker and Adrian Kent elaborated on the concept further. At least here reduction to one state is recognized while in many worlds of Everett reduction does not occur. In multiverse every possible state starts a new history.

More in the super –position domain

The other dilemma is when and where and in what level this transformation to reduced state is happening. Please note that mathematics of superposition is continuous where as reduction represents a discontinuity and change in state vector.⁵⁶

So the coarse grain (superposition) has to be in a continuous media where as the projected reduced state has to be in a discrete background. In proposed model space-time is discrete and elements in proposed singularity have a continuous nature. So again in my interpretation, the course grain state (superposition) happens in singularity and exists at informational level. The refined and reduced state is projected and materialized to our space-time. So boundaries of space time are where transformation actually happens. This is in line with the Copenhagen Interpretation of Quantum Mechanics as originally suggested by Neils Bohr. He believed superposition takes place at the mind of observer in informational state. Reduction occurs when we refine the information.

Do we need to extend the superposition to macroscopic world and then fall into the doldrums of infinite number universes, which are growing enormously by instant? Even thinking about it makes one insane. My humble suggestion is to consider the super position presence somehow out of our universe. Let us then take the state reduction as an event inside our physical world. This way we are left only with one universe. This is in line with our observation.

Here are the main questions: Are we going to take the every moment experience with mind behavior as a main portion of reality and accepting it as model to clarify the obscure portions of physical world?

Or do we keep trying to include implausible fantasies, like many universes or multiple histories (the idea that every event that could happen in the past actually happened) as part of reality? What I am suggesting in here is to find a solution by simply opening out the scope and include a mind like entity as a contributing domain. Just like mathematicians who when they could not solve problems in existing domain, opened out their scope and added negative numbers or imaginary number domains and opened the gridlock.

Observer and Quantum State Reduction

Experiments show that the act of measurement by the experimenter will reduce the super position of state to one definite state. If we open the door in Schrödinger box we find the cat either dead or alive and never both.Is it the measuring or measurer who changes the overlapped different states to one single one?

The founder of quantum mechanics Neils Bohr explains the state reduction,

“We customarily think of the outside world as separate from ourselves, and the boundary between the two is the surface of our skin. However, think of a blind person who gets around with the assistance of a cane. In time that person will probably treat the cane as part of his or her body, and will think of the outside world as beginning just at the tip of the cane. Now imagine the blind man's sense of touch extending out of the tip of the cane and into the roadway itself. Imagine it extending further, down the block, into the countryside, to the whole world. There is no point where the blind man ends and the world begins. Similarly, we can not say which is the system and which is us observing it.”

Therefore, he believed that our body is physically extended through out the universe and we actually are the universe. According to him there is no boundary and we are the whole system.That is why we can affect the world and induce state reduction.

On the contrary, Evan Walker believes,

“…the system undergoes state vector collapse because of our mind. This effort to obtain an entirely practical interpretation of quantum mechanics … lead us to the incredible conclusion that mind, or consciousness, affects matter.”⁸

State reduction is not the only place where the measurer and the act of measuring influence the quantum mechanics. The observer also affects quantum entanglement. In entanglement two or more subatomic particles are connected to each other even if they are worlds apart. If the observer reduces the spin of one of them to a definite state, the spin of the other particles changes accordingly and immediately. Considering the history of particles in the world logically each particle should have countless entanglements with countless particles which it encountered in its past history.

Surprisingly, when a physicist begins the entanglement experiment between a pair of particles any preexisting entanglement is eliminated and just the entanglement between two particles under experiment is observed. So we as experimenters are changing the world even at the quantum level.

Understanding how human can affect quantum mechanics is not easy. It has created many controversies. One wonders, if the principle can be applied in everyday life.Can we change the world at our will? Many new school of thoughts are advocating the idea.

One of them believes that the history and the state of the world depend on our question. We see the answers, which are in line with what we are looking for.Others like Lee Smolin believe there is “one universe seen by many observers, rather than many universes, seen by one mythical observer outside the universe.”²⁷

State Reduction and Dream Elucidation

Copenhagen interpretation of quantum mechanics first suggested by Neils Bohr, has gained popularity against the other theories despite its very strange sketch. It talks about how an observer would collapse superposition of particle properties into a definite and objective state. Arnold Mindell compares these phenomena with fantasy and its overlapped states versus a definite state found in consensus reality. He claims:

“Another method of marginalizing experience occurs when you start thinking about the meaning of the fantasy, while in the midst of the fantasizing. Thinking about it stops the fantasy.”¹⁴ and we are back to one state world that we call reality.

Singularity and State Reduction

Lee Smolin believes that we are seeing the same universe from different angles. At the beginning of this paper I was trying to draw an entity with zero dimension where the image of all of the points in our world can drop in it and stay superimposed. Some place where different events can happen simultaneously because the notion of time is not present. May be we don't have to speculate in remote and strange thought domains.Multiple universes and multiple histories do not sound very logical. Rather we can assume an intimate proximity and relationship between macrocosm and singularity. With this assumption, multiple states stay in one arena, which has the capability to accommodate them. This way we do not have to mix it up with activities, which are allowable in space-time and macrocosm. Otherwise, it leads to confusion and we will be dragged into an in-deterministic physics that nobody knows how to deal with it.

Dr. Walker rejects the measurement error interpretation by reasoning that our measuring device is only another sub-atomic particle, which according to Schrödinger’s equation entangles with the particles under observation. This should add to complexity of superposition, not state reduction. At the beginning we explored the similarities between mind and proposed singularity. The necessity to utilize complex numbers in order to explain quantum behavior suggests that elements in imaginary world participate in determining quantum physics. Previously, I took the imaginary portion, to represent the effect of the proposed singularity.

My conjecture is that the physical world is made of separate and discrete parts and bodies. But the duality nature of the existence connects and interacts each part through the universal consciousness.The universal consciousness is extended through our bodies as well and this is how we are connected and mingled with the whole.

Tonomura Double Slit Experiment:

Feynman's Sum over Paths Approach

In Thomas Young’s double-slit experiment a beam of light is directed towards a barrier with two slits that diffract the beam. A screen is installed behind the barrier that shows light and dark rows or the so-called interference pattern.This is the basic experiment, which shows the wave property of light.In 1920, Albert Einstein received the Nobel Prize for introducing the photon as a packet of light energy. Thereafter, light has been considered as a particle wave function. Photon is the particle portion of light.

Tonomura Double slit experiment is almost a similar experiment but with a very strange result. In this experiment, electrons are fired one by one in time intervals of ten seconds. Interestingly, the interference pattern appears in the screen similar to the one when a bunch of electrons is fired towards both slits simultaneously. The experiment has been repeated by many researchers. Brian Greene explains how the strange results were first observed:

“In 1920 Davisson and Germer ...were studying how a beam of electron bounces off a chunk of nickel. The nickel crystals in such an experiment act very much like the two slits in the double slits experiment of Thomas Young... Their experiment therefore showed that electrons exhibit interference phenomena... even if the beam of fired electrons was thinned so that, for instance, only one electron was emitted every ten second, the individual electron still built up the bright and dark bands.”¹

In order to explain the electron two-slit paradox the Late Physicist Richard Feynman proclaimed:

“Each electron that makes it through to the phosphorescent screen actually goes through both slits. Feynman argued in traveling from the source to a given point on the phosphorescent screen each individual electron actually traverse every possible trajectory simultaneously…It goes in a nice orderly way through the left slit. It simultaneously also goes in a nice orderly way through the right slit. It heads toward the left slit, but suddenly changes courses and heads through the right. It meanders back and forth, finally passing through the left slit. It goes on a long journey to Andromeda galaxy before turning back and passing through the left slit on its way to the screen. And on it goes- the electron, according to Feynman, simultaneously sniffs out every possible path connecting its starting location with its final destination.”¹

Of course, this is not his personal opinion. Different experiments suggest the above conclusion. The so-called Diffraction Grating Mirror works with the same principle.

Broken Mirror
The reflection angles do not match. However, a detector placed out of range can still register a signal.⁵²

In addition, the above explanation is obviously against the Special Relativity that limits the velocity to light speed. If the electron is going back and forth in different ways, it should have infinite fold time speed of light, which is contradicting the known space-time physics.

Singularity and Tonomura Double Slit Experiment

To have an infinite speed, the particle has to perform in a non-local arena. A better explanation can be reached, if we accept that the electrons are acting in a field with no time dimension. In this situation, speed conflict is solved but the paradox is still not completely resolved. One has to delete the notion of space and distance out of this experiment as well. This way the electron can come from everywhere and nowhere. Using the verb come applies to travel in space. It is better to use appear and accept that in this experiment electrons pop in and out of space-time universe.

On above interference experiment, Feynman tried to explain the paradox by claiming that each electron will follow all possible tracks before it hits the screen. We can claim that here, the electron follows the non-locality characteristic of the proposed singularity.Either non-locality or being not time-bound can explain this effect more logically than assuming that electron traveled along all possible trajectories before hitting the screen. Roger Penrose offers the mathematic equation for two-slit experiment by using complex numbers for quantum state. Roger Penrose writes:

“They can be represented on a two-dimensional plot with the purely real numbers running along the x-axis, and the purely imaginary numbers running up the y-axis, the imaginary axis.”⁵

To introduce the mathematics Roger Penrose has to use imaginary dimension along real dimension. He could not find any real dimension in our space-time universe, which can help him to mathematically explain the phenomenon. Again, we can imagine the complex numbers in our mind. But quantum two-slit behavior is happening all over the world in every moment, even if, our mind is not with it. There should be another being out there to accept the image, to be able to accommodate the imaginary dimension of complex numbers.Can we suppose that singularity is there to do it for us?

One can assume that if complex numbers represent particle functions, then particles themselves have to have an imaginary (out of space-time) phase.

Abstract World of Mathematics

Roger Penrose uses the Argand Diagram (presented in the Complex Number chapter) to discuss the complex numbers behavior.

“The fact that these numbers are built into the foundation of quantum theory often makes people feel that theory is a rather abstract and unknowable kind of thing, but once you get used to complex numbers, particularly after playing around with them on the Argand diagram, they become very concrete objects and you do not worry so much about them.”⁵

Therefore, Professor Penrose is suggesting staying in the abstract world of mathematics and viewing the imaginary number as a component of Argand diagram which is drawn in front of us.

If we try to understand the meaning of complex numbers with our space-time knowledge, we will face a concrete wall. Therefore, we choose to take refuge in mathematical domain. We tend to take imaginary number as a mathematical entity and give ourselves comfort.From school times we have learned how to use numbers as abstract entities. We are used to perform mathematical calculations and ignore their relation with objective reality. We cannot stay in this refuge for long. Our father Adam didn't. We cannot do it either. We have to explore, find and assign a tangible and deterministic reality to imaginary and notion of complex numbers. On the other hand because mathematics are so precise in calculating the Newtonian physics, electromagnetism, GTR and quantum mechanics, if in some parts it does not match our perception of reality, one could suspect that our perception might be wrong or incomplete.

In our model, because, there is no dimension in singularity an electron can move radially -- in and out of space-time universe, but yet cover the whole angular range, because singularity is everywhere and nowhere. An electron being at the same time in singularity, can defy 'steel ball' or ‘Classical’ interpretations of stationary orbital as perpetual motion in our space-time universe. In this explanation an electron does not need to follow the laws of classical physics.

Quantum Entanglement

Different Quantum Mechanical experiments have proved that pair of particles, which traveling back to back in opposite direction even if they are worlds apart, are entangled. Any change implicated to any of them will instantly change the other particle accordingly. It is interesting that the change occurs instantly.

This is one of the discrepancies between the Special Theory of Relativity and Quantum Mechanics. According to Special Relativity, nothing can travel faster than light. Instant connection between two spatially separate objects observed in Quantum Mechanics, is in contrast with the principles of the Special Relativity.

Professor Roger Penrose describes the entanglement as:

“Modern preoccupation with action-at-a-distance (to which Einstein objected) revolves around a purely quantum phenomenon. This is the celebrated thought experiment in which an 'entangled' system of two objects is created. The wave function of object # 1 is correlated with the wave function of object # 2. By the axioms of quantum mechanics a measurement of the properties of object #1 forces its wave function to collapse, instantly implies a correlated collapse in object #2 though it be arbitrarily far away.”⁵

Brent Nelson, M.A. Physics, Ph.D. Student, UC Berkeley writes: “Non-local effects...occur in quantum mechanics and they cannot be understood in terms of one thing being separate from another - some sort of global activity is taking place.”

Scientists have been puzzled by this strange phenomenon. Action at the distance without any apparent link also exists in electromagnetic field or gravity field. In case of quantum entanglement, no logical explanation, which can be agreeable by all, has been offered so far.

Aspect’s Experiment

Alain Aspect and colleagues in 1982 experimentally proved the reality of Quantum Entanglement, and the non-local actions.The diagram below sketches the experiment for more detail, please refer to http://roxanne.roxanne.org/epr/index.html or other related academic books and resources.

Aspect’s experiment for quantum entanglement²⁵

Allan Aspect designed and performed the above experiment to examine the concept of quantum entanglement.

A similar experiment has been repeated in different parts of the world since then. They all proved the entanglement exists between pair of particles that are far apart in space. Albert Einstein struggling to stick to a deterministic world suggested that there are contributing variables at work that produces this effect. He believed these variables are hidden from us because of our limited knowledge. However, the hidden variable explanation for the entanglement has been proved wrong by different experiments. Entanglement exists without any space-time link.

Quantum physics tells us that two particles are not differenttheir own individual properties. Rather, the two particles are entangled together and express a seamless unity. Here, the notion of identity and locality no longer applies.

Singularity: The Media for Quantum Entanglement

George Greenstein and Arthur G. Zajong write “Hidden behind the discrete and independent objects of the sense world is an entangled realm.”¹¹

We are looking for a realm where entanglement and unity of distant objects can take place. If by our assumption, singularity collects remote distances of our universe in one spot (singularity itself) action at a distance can be simply described. Look at an analogy of image of a landscape in a two-dimension mirror. The images of the objects, which are far apart in three-dimensional world, but are in a line perpendicular to surface of the mirror, are superimposed and in contact with each other in two-dimentiality of a mirror.As previously mentioned in no-dimension, all points will fall on top of each other. One may argue that the images fall on each other not real objects. The above statement is true, but image is carrying the information. Informationis not separate from object itself. In one view, the object is information in its totality.

Please note that, originally we have assumed that the world has a dual and complimentary nature, an objective nature and a subjective imaginary nature. These two aspects of the reality intermingle and create the world.Therefore, in this view the image is just another expression of the object.

In the Wave-function Chapter, I have assumed that objects enter informational domain (singularity) during each wavelength. The particles can exchange information instantly in this realm. Remember, there is no time element in the proposed singularity.

Ervin László, the famous Hungarian philosopher of science, postulated a similar scenario. He assumed quantum vacuum as a universal field that interact with matter.He asserts that the field:

The idea of space-time being embedded in a sea of something is nothing new. Paul Dirac also speculated that space-time is embedded in a sea of photon. He later on postulated that universe is embedded in a sea of negative electrons. However, such a sea has to have zero dimensions to be able to incorporate quantum entanglement. Singularity/Space-time duality with proposed description for wave particle function presented in this book provides such a zero size media where quantum entanglement can materialize.

The description of entanglement in this model is compatible with the Special Relativity because it infers that although a pair of particles may be far apart in space-time, in singularity domain they are related. Therefore, information does not actually travel beyond speed of light in space-time to reach the other particle.

This is another indication that the presented concept deserves attention.The explanation for action-at-a-distance is embedded in this model. As far as I know, there is not many theories out there that offers an explanation for quantum entanglement phenomenon.

Quantum Tunneling

Cassimir Effect
Courtesy of Nahid Sahel Gozin

During its wave function, if a particle encounters a barrier where it cannot occupy an energy state (can not be present in the space-time), it tunnels and appears on the other side of the barrier.Quantum tunneling also does not have any explanation with Newtonian Physics. An explanation can be offered for the phenomenon that is similar the one that I offered for wave particle function. In quantum tunneling if condition does not allow, the trace of particle will not resurface and stays in singularity and shows up again when the obstacle in space-time is bypassed.

Super-Luminal Speed

Quantum entanglement and quantum teleportation are examples of the ability of saving information and playing it back as needed. In recent research by Dr. Mohammad Mojtahedi, of the University of New Mexico Physics Dept., pulses have been measured which travel faster than speed of light in a vacuum. He measured pulses up to 2.38 times the speed of light. Although different interpretations and conclusions can be derived from this experiment, he attributes results to quantum tunneling effect. We have supposed that, in tunneling the trace of particle does not appear in space in time and leaps to farther location. Therefore, quantum leap can be the reason that light's speed limit is violated in this experiment. One may assume, in quantum leap, when the particle resurfaces the collective speed is more than light speed in space-time.

Telekinesis

Telekinesis practitioners claim that mind can move the objects in macroscopic world. The phenomenon is not scientifically confirmed yet. But its advocates claim that none of the four physical forces has been detected as a force behind the movement.

Quantum entanglement can create scientific explanation for many of the Para-psychological effects like telepathy or hypnosis.

Para-psychological activities are claimed and demonstrated, but we cannot explain them. Quantum behavior is repeatedly shown and recorded in numerous experiments and we are applying it to our advantage but we cannot explain it either. Consciousness is in us. It is the basis of our awareness, but still we cannot explain it. Certain basic mathematical functions and facts exist (like complex numbers) but they cannot be related to physical world in its totality. To understand the unexplained we have to be ready to look for new dimensions and domains.We have to be ready to travel to domains which goes beyond matter or other known physical properties, if needed.

Pascual Jordan, one of the major early contributors to quantum theory says: “We compel [the electron] to assume a definite position.”⁸

Who are we? Where do we stand in the equation? Can we come to the conclusion that our consciousness is the extension of singularity?

Can we claim that our will is creating the state vector collapse according to our desire?

Quantum Teleportation

We have watched the fantasy of the teleportation in the Star Trek series. The actual quantum teleportation is the transferring of tiny units of information, called quantum bits or qubits, about a particle. By transporting the information to another location, we can create a replica of the particle in new location. In quantum teleportation actual matter or energy are not transported.

This procedure was done inside laboratory in short distances. Samuel Braunstein, a professor of informatics at the University of Wales in Bangor, England was part of a team that teleported photons from one end of a table to the next in 1998.Nicolas Gisin, a physicist at the University of Geneva and his team teleported qubits carried by photons of 0.05 inch (1.3mm) wavelength in one laboratory onto photons of 0.06 inch (1.55mm) wavelength in another laboratory 180 feet (55 meters) away along 1.2 miles (2 kilometers) of fiber optic wire in January 2003. And most recently, Austrian researchers have teleported photons across the Danube River in Vienna. They reported their achievement in April 2004. Because of measurement problems created by uncertainty principle, teleportation in above experiments had to be performed by using entanglement principle of quantum theory. Below I am including one of the reports regarding this phenomenon provided by Daniel F. James from University of Innsbruck in Austria, in collaboration with a scientist at Los Alamos National Laboratory.

“In the experiment described in the scientific journal Nature, the group achieved teleportation using singly-ionized calcium atoms that were confined and cooled to ultra-low temperatures (around 15 millionths of a degree above absolute zero). Using lasers, the internal configurations of the atoms -- their quantum states -- were controlled very precisely, allowing entanglement between two of the atoms to be created. One of these entangled atoms was then further entangled with a third atom -- the input of the teleporter. By performing a simple measurement on this pair, and another series of interactions dependent on the outcome of the measurement, the original input state was then re-created on the remaining (output) atom. The quantum state teleportation experiments were carried out at the University of Innsbruck's Institute for Experimental Physics.”

Singularity and Teleportation

Please note that teleportation was performed by just transferring the information, not the actual particle. In other words for entanglement and teleportation, we need an information media. In this model, the proposed singularity acts as such media. Further more, the above experiments defies string theory interpretation of entanglement. Because in the above experiment a particle (being string or any other shape) is not responsible for entanglement and teleportation, rather phase transitions from particle to qubits and back to particle is shown to be the actual phenomena behind the process. This is in line with the wave-particle function model proposed in Wave-Particle chapter.

Concept Review: Quantum Fluctuation, Conservation Law and Mind

Let us discuss some of the conclusions derived from quantum theory; “In the nucleus there is a "sea of quarks", which continually pop into and out of existence in our Space-time universe due to quantum fluctuations.”

This violates the conservation of energy principle that we so dearly adhere to. Here we have to look beyond the space-time and open our vision to series of related events out of our universe. Above I suggested that energy can penetrate from Planck holes into the space-time and create the sea of quarks. Also matter can transform to energy and leave our space-time through the holes. Therefore, in this view the two-way transformation of energy and matter is suggested for quantum foam phenomena.

Quantum Foam

In addition, quantum fluctuation is comparable to mind activities during awakeness. During normal mind activities our consciousness is intermittently in and out of objective world. Our consciousness' constantly fluctuates between two different arenas. We are constantly alternating between sensation and imagination domains. In other words, our mind is constantly popping into and out of the physical world? We can also compare sleep dreaming and awakeness as an analogy. While we are awake we are time bonded and local. We also are dealing with objective reality most of the time. During sleep we depart from objective world and become non-local and floating out of time limits. Please refer to Quantum Mind by Arnold Mindell on the related topics.¹⁴

Dr. Mindell very clearly shows the many resemblances between mind activity and quantum behavior. There is no way that I can do any better.

Orbiting Electron

In the current understanding of the atom, an orbital is not something like the orbit of a planet around the sun. Orbiting electron is present at the same time in a whole region of space and has a whole range of velocities. It is a probability distribution in space. And, the electron cannot be said to be really 'moving'.

Current belief indicates that, electron does not follow a specific trajectory in its orbit to reach to a new position. This violates the locality rule in space. Experiments reveal that the electron only ever moves radially -- in and out.... But yet it covers the whole angular range. So this way, it defies steel ball rotation movement in classical physics. Alternatively, we can claim that, an electron in its orbit is everywhere and nowhere. If we cannot follow electrons trajectory, we have to come to conclusion that at times it is absent, and does not occupy a spatial location. If it does not follow the space-time rule of locality, may I suggest that electron or its trace travels to singularity and comes back to our space-time in different location according to the scenario explained in wave function chapter?

This interpretation brings the quantum mechanical experiments to more understandable and meaningful events.

Conclusion

If we take our universe as a closed system, in many quantum mechanical phenomena the first law of thermodynamics (conservation of energy) goes under question. Introducing virtual particles as quantum of energy fields does not satisfy the common sense. Either we have to drop universality of conservation of energy and matter or accept another entity which interacts with our universe.

In this view quantum arena is the twilight zone between the space-time universe and the proposed singularity. In other words, quantum domain is where space-time and singularity intermingle. This is why it demonstrates an objective reality mixed with subjective and imaginary realm.

The complimentarity between two observables of a particle like momentum and location is the same feature which manifests itself as either a singularity element (momentum-energy-) or locality (space-time feature).

Applying classical physics laws alone to explain quantum mechanics is doomed to failure. We need to mix classical logic with mind-like realm laws to be able to explain the unsolved mysteries of quantum mechanics.

Above I have explained different quantum mechanical paradoxes based on the above concept.

Summary

While quantum mechanics is very precise to predict and reproduces the results of experiments, it does not offer any explanation for the strange results obtained in the lab. Adding the proposed singularity as a non-local energy–information media offers explanations for the strange results by exposing us to a new paradigm. This paradigm delivers its own logic which can explain many of the current paradoxes.

Explanations for Tonomura’s two slit interference, quantum entanglement and other quantum mechanical phenomena has been proposed based on this model.